## 9 Oct 2011

### Solution for Practice Problems (GTF 101): Calculation for Gases

Q1:  If 4L of H2 gas at 1.43 atm is at standard temperature and the pressure was to increase by a factor of 2/3, what is the final volume of the H2 gas?  (Hint: Boyle's Law)
Solution
In order to solve this question you need to use Boyle's Law:  P1V1 = P2V2
Keeping the key variables in mind, temperature and the amount of gas is constant and therefore can be put aside, the only ones necessary are:
1. Initial Pressure: 1.43 atm
2. Initial Volume: 4 L
3. Final Pressure: 1.43x1.67 = 2.39
4. Final Volume(unknown): V2
Plugging these values into the equation you get:  V2= (1.43atm x 4 L)/ (2.39atm) = 2.39 L

Q2:  If 1.25L of gas exists at 35oC with a constant pressure of .70 atm in a cylindrical block and the volume were to be multiplied by a factor of 3/5, what is the new temperature of the gas?  (Hint: Charles's Law)
Solution
In order to solve this question you need to use Charles's Law: V1/T1 = V2/T2
Once again keep the key variables in mind.  The pressure remained constant and since the amount of gas is not mentioned, we assume it remains constant.  Otherwise the key variables are:
1. Initial Volume: 1.25 L
2. Initial Temperature: 35oC + 273.15 = 308.15K
3. Final Volume: 1.25L*3/5 = .75 L
4. Final Temperature: T2
Since we need to solve for the final temperature you can rearrange Charles's: T2 = (T1 X V2) / V1
Once you plug in the numbers, you get: T2= (308.15 K x .75 L)/ (1.25 L) = 184.89 K

Q3: At 655 mm Hg and 25.0oC, a sample of Chlorine gas has volume of 750mL.  How many moles of Chlorine gas at this condition?
Solution
P=655mm Hg; T=25+273.15K; V=750mL=0.75L
n = (PV) / (RT)
= [655 mmHg x (1 atm / 760 mmHg)] [0.75 L] / [0.0821 L. atm / mol. K] [25 + 273.15 K]
= 0.026 mol

Q4:  5.0 g of neon is at 256 mm Hg and at a temperature of 35º C.  What is the volume?
Solution
Step 1: Write down your given information:  P = 256 mmHg; V =?; m = 5.0 g; R = 0.0821 L·atm·mol-1K-1;  T = 35º C.

Step 2: Convert as necessary: 256 mmHg = 0.3368 atm; 5.0 g Neon = 5.0/ 20.18 g = 0.248 mol; 35º C = 308.15 K.

Step 3: Plug in the variables into the appropriate equation:

V = (nRT) / (P) = 18.63 L

Q5:  Find the volume, in mL, when 7.00 g of O2 and 1.50 g of Cl2 are mixed in a container with a pressure of 482 atm and at a temperature of 22º C.

Solution

Step 1: Write down your given information:  P = 482 atm; V = ?; n = ?; R = 0.0821 L·atm·mol-1 K-1; T = 22º C + 273.15 = 295.15K; 1.50g Cl2; 7.00g O2

Step 2: Find the total moles of the mixed gases:  n total = n O2  + n Cl2

= [7.00 g (1 mol O2 / 32.0 g O2)] + [1.50 g (1 mol Cl2 / 70.9 g Cl2)]
= 0.24 mol

Step 3: Now that you have moles, plug in your information in the Ideal Gas Equation:

V = (nRT) / (P) = 0.012 L = 12 mL.
Q6:  A 3.00 L container is filled with Ne (g) at 770mmHg at 27oC.  A 0.633g sample of CO2 vapor is then addedWhat is the partial pressure of CO2 and Ne in atm?  What is the total pressure in the container in atm?

Solution

Step 1: Write down all given information, and convert as necessary:  P = 770mmHg --> 1.01atm; V = 3.00L; n(Ne)=?; T = 27oC --> 300.15K; n(CO2)= ?

n (CO2) = 0.633 g CO2 (1 mol / 44 g CO2) = 0.144 mol CO2

Step 2: Find the unknown moles of Ne.

n (Ne) = PV / RT = 0.123 mol

Step 3: Now that have pressure for Ne, you must find the partial pressure for CO2. Use the ideal gas equation.

(PV / nRT) Ne = (PV / nRT) CO2

Since Volume (V) and Temperature (T) and the Gas Constant (R) are constants, you may remove them from the equation.

(P / n) Ne = (P / n) CO2, hence, (1.01 atm / 0.123 mol Ne) = (P / 0.144 mol CO2), hence, P CO2 = 0.118 atm

Therefore, P (total) = P (Ne) + P (CO2) = 1.01 atm + 0.118 atm = 1.20 atm

Q7:  What is the density of nitrogen gas (N2) at 248.0 Torr and 18º C?

Solution

Step 1: Write down your given information:  P = 248.0 Torr --> 0.326 atm; V = ?;  n = ?;
R = 0.0821 L·atm·mol-1 K-1; T = 18º C --> 291.15 K

1 mol of nitrogen is 14.01 g, hence 2 moles equal to 28.02 g

Step 2:  We need to manipulate the Ideal Gas Equation to incorporate density into the equation.

d = m/v = PM/RT

d = 0382 g/L